Particulates in plasmas are normally negatively charged in thermal equilibrium since the mobility of electrons is much higher than that of ions. Such charged particulates (I.e., dust particles) are commonly observed in plasmas in both nature and man-made devices. If the dust number density is sufficiently high and the kinetic energy per particle is less than the interparticle potential energy, the system is called to be in strongly coupled state. In this research project, under various coupling conditions, we have investigated dynamical properties (such as waves, diffusion, dissipation, fluctuations, etc.) for collective motions of plasmadust systems, using molecular dynamics (MD) simulations, in order to clarify properties of the system in the light of statistical dynamics. In 2001, we evaluated dynamical stress correlation functions of the Yukawa system, using MD simulations, and calculated shear viscosity of the system in the wide range of coupling parameters, using Green-Kubo formula. Since transport coefficients of the system are generally non-local in space and time under strongly coupled conditions, one may approximately express such coefficients with memory functions. In 2002, using MD simulations, we determined the memory function for shear viscosity. Especially if the dependence of memory function on the wave number can be ignored, the macroscopic behavior of the system can be described by the "generalized hydrodynamics (GH) equations". In the present work, we have determined the dependence of coefficients that appear in the GH equations on the thermodynamical parameters (such as the system temperature and screening length of the interparticle potential function) of the Yukawa system. With these results, we are now able to analyze dynamical properties of the Yukawa system under non-equilibrium conditions in the longwave and lowfrequency limit by solving the macroscopic equations